Optical pulses having a duration of a few femtoseconds or less may include only a few optical cycles at a fundamental carrier frequency of the pulse within an envelope of the pulse. A pulse-envelope typically has a Gaussian or Sech-squared form. The peak power within the envelope will depend on the phase of the carrier cycles relative to the envelope. This is referred to by practitioners of the art as the carrier envelope phase (CEP). FIG. 1A is a graph schematically illustrating a condition where the carrier is retarded in phase by an amount φCE with respect to the pulse envelope. The highest peak power will occur when a peak of one of the carrier cycles is exactly in phase (φCE=0.0) with the peak of the envelope. This is schematically illustrated in FIG. 1B. The less the number of cycles within the envelope, i.e., the shorter the pulse, the greater is this phase dependence of peak power in the pulse.
Techniques for stabilizing the CEP of a laser oscillator have long been known in the art. One such technique involves a closed loop feedback arrangement wherein the CEP is measured and compared with a desired value. Any difference between the measured and actual value is used to vary optical-pump power to a gain medium of the oscillator to drive the measured value back to the desired value. It has been found, however, that if a pulse from a CEP-stabilized oscillator is amplified in a chirped pulse amplification arrangement the CEP of the amplified pulses will usually not be stable. In such an arrangement input pulses from the oscillator are temporally stretched by a pulse stretcher from an original duration before amplification; amplified in an optical amplifier; and temporally compressed in a pulse compressor back to about the original pulse duration.
One approach to stabilizing output pulses from a chirped pulse amplification arrangement is disclosed in U.S. Publication No. 2010/0061411, incorporated herein by reference. Here, stabilization is effected by a closed loop arrangement in which the CEP is again measured and compared with a desired value. Any difference between the measured and actual value is used to vary the separation of gratings in the pulse stretcher or compressor of the amplifier to drive the measured value back to the desired value.
A problem with this and other prior-art approaches to CEP control in a master-oscillator-plus-amplifier system is that the approaches do not take into account that different factors contribute to total CEP instability. By way of example there may be a slow CEP drift due to thermal effects and higher frequency drifts due to mechanical resonances within the pulse stretcher, the optical amplifier, or the pulse compressor.
U.S. Pat. No. 7,701,982, granted to Yu et al., discloses an arrangement for a stabilizing the CEP of a modelocked oscillator, optically pumped by a beam from a pump-laser. Here, a balanced homodyne detection system is used in an f-2f interferometer to generate a CEP error signal that is used to stabilize the CEP of an ultrafast oscillator. Two parts of the error signal (one from each arm of the balanced homodyne detector arrangement) are processed by a first PID (proportional-integral-differential) controller (feedback circuit). A feedback signal from the first PID controller is split into two portions. A first of the two portions is fed to a second PID controller. A signal from the second PID controller is used to adjust a slow (low-frequency) response actuator in the oscillator, in this case, a prism located in the oscillator between resonator (laser-cavity) mirrors of the oscillator, and moveable by a piezoelectric transducer (PZT) in response to the signal from the second PID controller. The second of the two portions of the signal from first PID controller is fed to a fast-response) actuator outside of the laser cavity, which responds primarily to high-frequency components of the signal from the first PID controller. In this case, the actuator is an acousto-optic modulator (AOM) inserted in the pump-laser beam to precisely modulate the pump power delivered to a gain-element in the oscillator laser-cavity. This methodology is described as being effective at stabilizing the CE phase of a mode-locked oscillator.
One shortcoming of the arrangement of the Yu et al. patent is that the signal controlling the low frequency actuator is not independent of the signal controlling the high frequency actuator. Any adjustment of the gain of the first PID controller automatically adjusts the net gain of the first and second PID controllers in series. Another shortcoming of the arrangement of the Yu et al. patent is that there is no provision for selecting the frequency bands applied to the high-frequency and low-frequency actuators. The particular actuators selected primarily determine whatever frequency selection there is. Yet another shortcoming of the arrangement of the Yu et al. patent is that low-frequency control requires a movable element in the oscillator laser cavity. Moving this element during operation could interfere with the mode-locking of the oscillator. A further shortcoming of the disclosure of the Yu et al. patent is that it does not address the problem of controlling the CEP of an oscillator-plus-amplifier system. This is significant inasmuch as most ultrafast laser systems in use are oscillator-plus-amplifier systems.
There remains a need for a method and apparatus for controlling the CEP of an ultrafast oscillator-plus-amplifier laser system. Such a method and apparatus should be capable of dealing with above-described, frequency-dependent CEP instability sources while overcoming the shortcomings of the Yu et al. arrangement for oscillator control.